caa a22 4500 378860186 CHVBK 20180305123344.0 cr unu---uuuuu 161128s2003 xx s 000 0 eng 10.2478/cmam-2003-0010 doi (NATIONALLICENCE)gruyter-10.2478/cmam-2003-0010 Discontinuous Galerkin Discretization with Embedded Boundary Conditions [Elektronische Daten] The purpose of this paper is to introduce discretization methods of discontinuous Galerkin type for solving second-order elliptic PDEs on a structured, regular rectangular grid, while the problem is defined on a curved boundary. The methods aim at high-order accuracy and the difficulty arises since the regular grid cannot follow the curved boundary. Starting with the Lagrange multiplier formulation for the boundary conditions, we derive variational forms for the discretization of 2-D elliptic problems with embedded Dirichlet boundary conditions. Within the framework of structured, regular rectangular grids, we treat curved boundaries according to the principles that underlie the discontinuous Galerkin method. Thus, the high-order DGdiscretization is adapted in cells with embedded boundaries. We give examples of approximation with tensor products of cubic polynomials. As an illustration, we solve a convection-dominated boundary-value problem on a complex domain. Although, of course, it is impossible to accurately represent a boundary layer with a complex structure by means of cubic polynomials, the boundary condition treatment appears quite effective in handling such complex situations. This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. discontinuous Galerkin discretization nationallicence structured grid nationallicence irregular boundary nationallicence embedded boundary nationallicence Hemker P. W. Kruislaan 413, 1098 SJ, Amsterdam, The Netherlands. Hoffman W. KdV Institute for Mathematics, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands. Van Raalte M. H. KdV Institute for Mathematics, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands. Computational Methods in Applied Mathematics De Gruyter 3/1(2003), 135-158 1609-4840 3:1<135 2003 3 cmam https://doi.org/10.2478/cmam-2003-0010 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.2478/cmam-2003-0010 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hemker P. W. Kruislaan 413, 1098 SJ, Amsterdam, The Netherlands NATIONALLICENCE 700 1- Hoffman W. KdV Institute for Mathematics, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands NATIONALLICENCE 700 1- Van Raalte M. H. KdV Institute for Mathematics, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands NATIONALLICENCE 773 0- Computational Methods in Applied Mathematics De Gruyter 3/1(2003), 135-158 1609-4840 3:1<135 2003 3 cmam CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter